Which of the following is the equation a superscript left parenthesis 2 b plus 1 right parenthesis baseline equals 3 c minus d written in logarithmic form?

Question

(1 point)
Responses

log subscript a baseline left parenthesis 3 c minus d right parenthesis equals 2 b plus 1
Image with alt text: log subscript a baseline left parenthesis 3 c minus d right parenthesis equals 2 b plus 1

log subscript a baseline left parenthesis 2 b plus 1 right parenthesis equals 3 c minus d
Image with alt text: log subscript a baseline left parenthesis 2 b plus 1 right parenthesis equals 3 c minus d

log subscript left parenthesis 2 b plus 1 right parenthesis baseline a equals 3 c minus d
Image with alt text: log subscript left parenthesis 2 b plus 1 right parenthesis baseline a equals 3 c minus d

log subscript left parenthesis 2 b plus 1 right parenthesis baseline 3 c minus d equals a

Answer 1

To convert the equation \( a^{(2b + 1)} = 3c - d \) into logarithmic form, we follow the definition of logarithms: if \( a^x = y \), then \( \log_a(y) = x \).

In this case:

• \( a \) is the base,
• \( (2b + 1) \) is the exponent,
• \( (3c - d) \) is the result.

Thus, we can write:

\[ \log_a(3c - d) = 2b + 1 \]

Therefore, the correct logarithmic form of the given equation is:

log subscript a baseline left parenthesis 3 c minus d right parenthesis equals 2 b plus 1